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 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The trapezium rule is a way of estimating the area under a curve. We know that the area under a curve is given by integration, so the trapezium rule gives a method of estimating integrals."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's check this method for the next function: $$f(x) = ({e^x / 2})*(cos(x)-sin(x))$$ with $\\varepsilon = 0.001$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Result:  -22.12539445092147\n"
     ]
    }
   ],
   "source": [
    "import math \n",
    "import numpy as np\n",
    "\n",
    "n = 4 \n",
    "a = 2.\n",
    "b = 3.\n",
    "def f(x):\n",
    "    return  (math.e**x / 2)*(math.cos(x)-math.sin(x))\n",
    "\n",
    "def trapezoid(a,b,n):\n",
    "  z = (b-a)/n\n",
    "  i=a\n",
    "  s=0\n",
    "  while (i+z)<b:\n",
    "    s=s+f(i)\n",
    "    i=i+z \n",
    "  s=z*(f(a)+f(b))/2+s\n",
    "  print('Result: ',s)\n",
    "    \n",
    "trapezoid(a,b,n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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